Q. The angles of a quadrilateral are in the ratio $2:4:5:7$. Find the angles.

Q. In the adjoining figure, $ABCD$ is a square. if $\angle PQR={90}^o$ and $PB=QC=DR$. Prove that
$\angle QPR={45}^o$

Q. In the adjoining figure, $ABCD$ is a square. if $\angle PQR={90}^o$ and $PB=QC=DR$. Prove that
$PQ=QR$

Q. In the given figure, $$ABCD$$ is a square and $$\angle PQR={90}^{o}$$. If $$PB=QC=DR$$, prove that $$QB=RC$$

Q. In the figure, $$BM\bot AC$$ and$$DN\bot AC$$. If $$BM=DN$$, prove that $$AC$$ bisects $$BD$$.

Q. In the figure, $$ABCD$$ is a quadrilateral and $$AC$$ is one its $$AB+BC+CD+DA> 2AC$$ diagonals. Prove that

Q. If $$O$$ is a point within a quadrilateral $$ABCD$$, show that $$OA+OB+OC+OD> AC+BD$$

Q. In the figure, $$ABCD$$ is a trapezium in which $$AB\parallel DC$$. If $$\angle A={55}^{o}$$ and $$\angle B={70}^{o}$$, find $$\angle C$$ and $$\angle D$$.

Q. In the given figure, $$ABCD$$ is a square and $$\angle PQR={90}^{o}$$. If $$PB=QC=DR$$, prove that $$AB+BC+CD+DA> AC+BD$$

Q. In the given figure, $$ABCD$$ is a square and $$\angle PQR={90}^{o}$$. If $$PB=QC=DR$$, prove that $$AB+BC+CD> DA$$

Q. In the given figure, $$ABCD$$ is a quadrilateral in which $$AB=AD$$ and $$BC=DC$$. Prove that
$$AC$$ bisects $$\angle A$$ and $$\angle C$$.

Q. In the figure, $$ABCD$$ is a square and $$\triangle EDC$$ is an equilateral triangle. Prove that
(i) $$AE=BE$$
(ii) $$\angle DAE={15}^{o}$$

Q. Prove that the sum of all the angles of a quadrilateral is $${360}^{o}$$.

Q. In the given figure, $ABCD$ is a quadrilateral in which $AB=AD$ and $BC=DC$. Prove that
$\angle ABC=\angle ADC$

Q. In the given figure, $$ABCD$$ is a quadrilateral in which $$AB=AD$$ and $$BC=DC$$. Prove that
$$BE=DE$$

Q. Three angles of a quadrilateral are ${75}^o,{90}^o$ and${75}^o$. Find the measure of the fourth angle.

Q. The length of the diagonals of a rhombus are $24cm$ and $18cm$. Find the length of each side of the rhombus

Q. In the adjoining figure, $ABCD$ is a square. $A$ line segment $CX$ cuts $AB$ at $X$ and the diagonal $BD$ at $O$ such that $\angle COD={80}^{\circ }$ and $\angle OXA=x^{\circ }$, then the value of $x$ is

1. ${125}^{\circ }$
2. ${120}^{\circ }$
3. ${130}^{\circ }$
4. ${140}^{\circ }$

Q. In the adjacent figure $ABCD$ is a parallelogram and $E$ is the midpoint of the side $BC$. If $DE$ and $AB$ are produced to meet at $F$, show that $AF=2AB$

Q. If an angle of a parallelogram is four-fifths of its adjacent angle, find the angles of the parallelogram